What are the divisors of 2290?

1, 2, 5, 10, 229, 458, 1145, 2290

There is a total of 8 positive divisors.
The sum of these divisors is 4140.
The arithmetic mean is 517.5.

4 even divisors

2, 10, 458, 2290

4 odd divisors

1, 5, 229, 1145

How to compute the divisors of 2290?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2290 by each of the numbers from 1 to 2290 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2290 / 1 = 2290 (the remainder is 0, so 1 is a divisor of 2290)
2290 / 2 = 1145 (the remainder is 0, so 2 is a divisor of 2290)
2290 / 3 = 763.33333333333 (the remainder is 1, so 3 is not a divisor of 2290)
...
2290 / 2289 = 1.0004368719965 (the remainder is 1, so 2289 is not a divisor of 2290)
2290 / 2290 = 1 (the remainder is 0, so 2290 is a divisor of 2290)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2290 (i.e. 47.853944456022). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2290 / 1 = 2290 (the remainder is 0, so 1 and 2290 are divisors of 2290)
2290 / 2 = 1145 (the remainder is 0, so 2 and 1145 are divisors of 2290)
2290 / 3 = 763.33333333333 (the remainder is 1, so 3 is not a divisor of 2290)
...
2290 / 46 = 49.782608695652 (the remainder is 36, so 46 is not a divisor of 2290)
2290 / 47 = 48.723404255319 (the remainder is 34, so 47 is not a divisor of 2290)